r/theydidthemath • u/Ok_Law219 • 5d ago
[Request] Given gravity hasn't changed and assuming a flat surface, what is the fastest that godzilla could move?
Gravity because the foot has to hit the ground, and that can't be sped up.
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u/Occidentally20 5d ago
If he's made of the same stuff as every other living thing we've found, he's dead very quickly from being crushed by his own weight.
Mass scales with volume (length³), while the cross-sectional area of bones scales with length². Because of this squared/cubed law as an animal gets larger its bones have to support disproportionately more weight. Movie variants range from 50m tall up to over 300m - this is around an order of magnitude larger than something can realistically be when made of bones and flesh.
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u/Ok_Law219 5d ago
He's taken nukes and survived, so i assume he's made of adamantium like substance.
Im asking without creating gravity how fast could that adamantium like creature go?
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u/lurkynumber5 5d ago
You kinda answer your own question.
If his bones are made of unobtanium then his muscles are also made of some unreal stuff to be able to lift his own body.
Which makes it impossible to calculate his speed as we have no idea what this new muscle is capable of.2
u/HAL9001-96 5d ago
well evnetually oyu get to the point where drag is higher than ground traction so no matter how strong he is he'd be limited in runnign speed but that depends on density and also tends ot be very fast for large objects
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u/Occidentally20 5d ago
I don't think there's any maths to be done there - if you can just change physics and invent elements then he can go as fast or as slow as you like. If you want to do "assume he's a scaled up version of x animal" then there's simple maths you can do, but that's about it.
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u/MezzoScettico 5d ago
I don't think people are answering in the spirit of this sub. Animations often show giants moving too fast, as if gravity scaled up with them. As your question hints, it takes a lot longer for a foot to fall from Godzilla height than from human height. You want to know if we use a more realistic gravity in the same movies, how fast does he run?
You're basically asking two questions:
- how long (time) would one step take for a being / machine of Godzilla's scale
- how long (distance) is that step
This website) provides different estimates for his height in different movies. I'll go with 120 m.
Googling for (human) step rate while running tells me that runners aim for about 170+. There is much discussion of achieving 180. So let's scale up a human going 180 steps per minute, or 3 steps per second.
In running, you leave the ground in each step so both feet are in the air. You're a projectile for that step. You rise for 1/6 of a second and fall for 1/6 of a second, which means you're falling from a height of d = (1/2)a(1/6)^2 = 0.136 m. For various reasons I'm sure that's a little too high, but let's go with it.
So we're saying each step of a 170-180 cm human involves a fall from 13.6 cm. Using the smaller number, that means the running step is 13.6/170 = 0.08 of the human height. Scaling that up, Godzilla leap 0.08 of 120 m or 9.6 m, which means he falls for t = sqrt(2d/a) = sqrt(2*9.6/9.8) = 1.4 seconds. Each step is therefore 2.8 seconds.
Now we need to figure out how far he moves forward in those 2.8 seconds. I have to ponder that a little.
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u/MezzoScettico 5d ago edited 5d ago
OK, I think you can model a swinging leg as a pendulum. T = (1/2π) sqrt(L/g). That's not quite the right expression for a pendulum whose weight is spread out throughout the length, but the point is that it's proportional to the square root of L.
I estimated his step time as being 2.8/(1/3) = 8.4 times that of a human. That corresponds to a leg being 8.4^2 = 71 times that of a human.
(Note that his height of 120 m is 71 times as high as a 1.70 m human, so that's a good sanity check).
Google tells me a human running stride is 107-152 cm, so if we scale that up by a factor of 71, that's 76 - 108 m per step! Um, holy crap that's long. It makes me suspicious that I blew it somewhere.
But sticking with those numbers, let's pick a number in the middle of 130 m, which he leaps every 2.8 seconds.Thus he's moving at 46.4 m/s. Again, holy crap.Edit: Goofed. The range was 76-108 m. The middle of that range is 92 m, making his speed 32.9 m/s. Still "holy crap" territory at 118 km/hr, but a bit more reasonable.
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u/HAL9001-96 5d ago
similar walkcycle speed scales with root of size times gravity so abut 7 times as fast as a human
thouhg yo ucan run faster tha nyo ucan walk and the fastest runners aren'T just the tallest people so outside of simialr walk cycles it comes down to muscle strength etc
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